Hong Life CalculatorsUnderstanding the ballistic coefficient calculator — concept and principle
The ballistic coefficient compares how much mass an object carries with how much drag it creates. A higher value means the object slows down less in air. This calculator uses the aerospace definition, applied to satellites, re-entry capsules and falling bodies, and also gives drag force, deceleration and terminal velocity.
How it is calculated
- β = m ÷ (CD × A), in kg/m² (× 0.204816 for lb/ft²).
- Drag D = ½ ρ v² CD A; drag deceleration = D ÷ m = ρ v² ÷ (2β).
- Terminal velocity, where drag equals weight: vt = √(2βg ÷ ρ), with g = 9.80665 m/s².
- If you enter a diameter, the frontal area is π d² ÷ 4.
The principle
Drag grows with frontal area and drag coefficient, while inertia grows with mass. Dividing one by the other tells you how strongly air affects the motion. Two objects with the same β follow the same trajectory in the same air, whatever their size. The sporting "BC" printed for bullets is a different, normalised quantity relative to a standard reference shape and is not computed here.
Worked example
Default inputs: mass 1.33 kg, CD = 2.2, frontal area 0.01 m² (a 10 cm cube), air density 1.225 kg/m³, speed 30 m/s.
- β = 1.33 ÷ (2.2 × 0.01) ≈ 60.45 kg/m², or 12.38 lb/ft²; mass per area = 133 kg/m².
- Drag at 30 m/s = ½ × 1.225 × 30² × 2.2 × 0.01 ≈ 12.13 N.
- Deceleration = 12.13 ÷ 1.33 ≈ 9.118 m/s², or 0.9298 g.
- Terminal velocity = √(2 × 60.45 × 9.80665 ÷ 1.225) ≈ 31.11 m/s.
| Drag coefficient C_D | Ballistic coefficient β (kg/m²) |
|---|---|
| 0.55 | 241.8 |
| 1.1 | 120.9 |
| 1.65 | 80.61 |
| 2.2 | 60.45 |
| 2.75 | 48.36 |
| 3.3 | 40.3 |
| 4.4 | 30.23 |
How to read the result
At 30 m/s the drag is almost equal to the object's weight, which is why the speed is close to the terminal velocity. Satellites with a low β lose altitude faster in the thin upper atmosphere; re-entry capsules are designed with a low β so they slow down high up where heating is manageable.
Common mistakes
- Confusing the aerospace β with the sporting bullet BC.
- Using a CD measured for a different shape or flow regime.
- Using sea-level air density at altitude.
- Mixing up area and diameter inputs.
Frequently asked questions
What does a high ballistic coefficient mean?
The object is heavy for its drag, so air slows it less.
How is terminal velocity related to β?
vt = √(2βg ÷ ρ); doubling β raises terminal velocity by about 41%.
Is this the same as a bullet's BC?
No. Bullet BCs are normalised to a reference projectile and have different units.
Sources: Anderson, J. D., Introduction to Flight, McGraw-Hill (drag) · Vallado, D. A., Fundamentals of Astrodynamics and Applications (ballistic coefficient and drag)